Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's

Pages: 1473 - 1506, Volume 17, Issue 5, July 2012

doi:10.3934/dcdsb.2012.17.1473       Abstract        References        Full Text (544.5K)       Related Articles

Konstantinos Chrysafinos - National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mathematics, Zografou Campus, 15780, Athens, Greece (email)
Efthimios N. Karatzas - National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mathematics, Zografou Campus, 15780, Athens, Greece (email)

Abstract: A discontinuous Galerkin finite element method for an optimal control problem having states constrained to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. It is shown that under suitable assumptions, the error estimates of the corresponding optimality system are of the same order to the standard linear (uncontrolled) parabolic problem. These estimates have symmetric structure and are also applicable for higher order elements.

Keywords:  Symmetric error estimates, discontinuous Galerkin, distributed control, semi-linear parabolic PDE's.
Mathematics Subject Classification:  Primary: 65M60, 49J20.

Received: September 2011;      Revised: December 2011;      Published: March 2012.

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